Distributed quasi-monotone subgradient algorithm for nonsmooth convex optimization over directed graphs

Distributed optimization is of essential importance in networked systems. Most of the existing distributed algorithms either assume the information exchange over undirected graphs, or require that the underlying directed network topology provides a doubly stochastic weight matrix to the agents. In t...

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Bibliographic Details
Published in:	Automatica (Oxford) Vol. 101; pp. 175 - 181
Main Authors:	Liang, Shu, Wang, Leyi, Yin, George
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.03.2019
Subjects:	Directed graph Distributed optimization Nonsmooth convex optimization Quasi-monotone subgradient algorithm Quasi-monotone subgradient algorithm Distributed optimization Nonsmooth convex optimization Directed graph
ISSN:	0005-1098, 1873-2836
Online Access:	Get full text
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Summary:	Distributed optimization is of essential importance in networked systems. Most of the existing distributed algorithms either assume the information exchange over undirected graphs, or require that the underlying directed network topology provides a doubly stochastic weight matrix to the agents. In this brief paper, a distributed subgradient-based algorithm is proposed to solve nonsmooth convex optimization problems. The algorithm applies to directed graphs without using a doubly stochastic weight matrix. Moreover, the algorithm is a distributed generalization and improvement of the quasi-monotone subgradient algorithm. An O(1∕k) convergence rate is achieved. The effectiveness of our algorithm is also illustrated by a numerical example.
ISSN:	0005-1098 1873-2836
DOI:	10.1016/j.automatica.2018.11.056